To answer your question, first find r the GCD of two given polynomials p and q, then, u=p/r, v=q/r and w=u*v.
The partial fraction expansion (PFE) of 1/w will give 1/w=y/u+x/v,
where the two desired polynomials x and y can thus be determined after performing reverse PFE. Thus,
1 = x*u+y*v, or
In addition, we may also find the two polynomials t and s, so that
It is interesting to note that x and y are expected to be, respectively, equal to 1/t and 1/s. However, it isn't so !
Please let me know if you want find out more detail derivation about these relations.
I would like a favor.I've made a gui that represents the gcd
it is like this: r=poly_gcd(p,q)
i've been asked to make this:
if you understand can you tell me how to show this expression out of the gcd code
I do not understand your question. But if you means that you want make a gui from my article, you may go ahead to do so.
Please see my other articles, such as "Solve multiple-root polynomials' that may refer computation of polynomial GCD.